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The reversible jump algorithm is a useful Markov chain Monte Carlo methodintroduced by Green (1995) that allows switches between subspaces of differingdimensionality, and therefore, model selection. Although this method is nowincreasingly used in key areas (e.g. biology and finance), it remains achallenge to implement it. In this paper, we focus on a simple sampling contextin order to obtain theoretical results that lead to an optimal tuning procedurefor the considered reversible jump algorithm, and consequently, to easyimplementation. The key result is the weak convergence of the sequence ofstochastic processes engendered by the algorithm. It represents the maincontribution of this paper as it is, to our knowledge, the first weakconvergence result for the reversible jump algorithm. The sampler updating theparameters according to a random walk, this result allows to retrieve thewell-known 0.234 rule for finding the optimal scaling. It also leads to ananswer to the question: "with what probability should a parameter update beproposed comparatively to a model switch at each iteration?"

Weak Convergence and Optimal Tuning of the Reversible Jump Algorithm